This is because, H20 has hydrogen bond between it's molecule (H-O-H------H-O-H) while H2S has weak Van Der Wals forces between it's molecule.Hence the molecules of H2O are strongly packed than H2S.
I know one often expects that water would be a gas at room temperature because of its low molecular weight in comparison to H2S which is much heavier than it. However, it is the polarity of the water molecules that make it a liquid at room temperature. The water molecule is dipolar because of the great difference in the polarities of oxygen and hydrogen. Thus, the hydrogen bonds that develop between the molecules as a result of this make water a liquid. Similarly, the hydrogen bonds are fairly weak between hydrogen sulphide molecules (because of a smaller dipolar moment of the molecule) and so, these can not bind to each other tightly enough to be called a liquid.
I was just going to point out the difference in MW between O and S. I didn't look up the bond strength of sulfur ATOMS and Oxygen ATOMS (not molecules) to hydrogen but it may be H-O is stronger than S-O since for one, the nuclei are further apart. Hence the overall size of H2S is larger than H2O so unless under pressure, H2S remains a gas at RT.